Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
234 conjugacy classes of subgroups; only the 59 normal subgroups are shown.
This group has 234 conjugacy classes of subgroups — too many to draw. Only its 59 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #27161484 | C2 | semidirect |
| 4. #27161289 | C2 | semidirect |
| 5. #27160824 | C2 | semidirect |
| 7. Q8⋊C8×C197 | C2 | semidirect |
| 57. D788 | Q16 | semidirect |
| 92. C197 | #1649 | semidirect |
| 99. Q8⋊C8 | D197 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×D788 | 2 |
| #27161484 | 2 |
| #27161360 | 2 |
| #27161289 | 2 |
| #27160824 | 2 |
| #27160808 | 2 |
| Q8⋊C8×C197 | 2 |
| #1649 | 197 |